Superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear $\ensuremath{\beta}$ decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model

Superallowed $0^{+} \to 0^{+}$ nuclear $β$ decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model

J. C. Hardy and I. S. Towner

Phys. Rev. C 79, 055502 – Published 26 May 2009

Abstract

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed $0^{+} \to 0^{+} β$ decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references, either because they have been superseded by much more precise modern results or because there are now reasons to consider them fatally flawed; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections, which were motivated by these new Penning-trap results. Third, our calculation of the statistical rate function $f$ now accounts for possible excitation in the daughter atom, a small effect but one that merits inclusion at the present level of experimental precision. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new “corrected” $F t$ values are impressively constant and their average, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, $V_{ud} = 0.97425 \pm 0.00022$ . The unitarity test on the top row of the matrix becomes $| V_{ud} |^{2} + | V_{us} |^{2} + | V_{ub} |^{2} = 0.99995 \pm 0.00061$ . Both $V_{ud}$ and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of $V_{ud}$ is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents, and extra $Z$ bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.